Hyperbola and parabola examples | Conic sections | Algebra II | Khan Academy

TL;DR

Learn how to find the vertex of a parabola using an intuitive approach in algebra.

Transcript

We're on problem 39. And it says which ordered pairs the vertex of f of x is equal to x squared plus 6x plus 5? Now, finding vertexes of parabolas, there's a formula, and negative b over 2a, but you might forget that when you turn 30 years old. The whole goal of this isn't just to pass an algebra exam. It's to learn algebra. Then when you learn cal... Read More

Key Insights

• ❎ The vertex of a parabola can be found using the formula -b/2a or through completing the square.
• 🆘 Understanding the intuition behind finding the vertex helps in mastering algebra.
• 💁 Writing a function in the form f(x) = A(x + or - b)^2 + C helps identify the vertex.
• 👻 Completing the square allows us to turn a function into the desired form.
• 😥 The minimum or maximum point of a parabola is at the vertex.
• ❓ The formula for finding the vertex becomes easier to remember with practice.
• ❣️ Asymptotes of hyperbolas can be determined by observing how the x and y terms approach infinity.
• 📈 Hyperbolas have asymptotes that the graph approaches but never reaches.

Questions & Answers

Q: What is the formula for finding the vertex of a parabola?

The formula is -b/2a, but it is better to understand the intuition behind it. The vertex occurs when the term inside the square is equal to 0.

Q: How do you complete the square to write the function in the desired form?

To complete the square, you need to find a value to add or subtract that will make the coefficient of the squared term half of the coefficient of the x term. This will allow you to create a perfect square.

Q: What is the equation of the vertex for the function f(x) = x^2 + 6x + 5?

We complete the square to write the function as (x + 3)^2 - 4. The vertex occurs when (x + 3) = 0, so the vertex is at (-3, -4).

Q: Can you use the formula -b/2a directly to find the vertex?

Yes, using the formula -b/2a for the function f(x) = x^2 + 6x + 5, we get -6/2 = -3. This also gives us the vertex (-3, -4).

Summary & Key Takeaways

• To find the vertex of a parabola, write the function in the form f(x) = A(x + or - b)^2 + C, where the vertex is (b, C).

• Complete the square to turn the function into the desired form.

• The vertex occurs when the term inside the square is equal to 0.

• The minimum or maximum point of the parabola is at the vertex.